Diffractive optical element, projection device, and measurement device

ABSTRACT

A diffractive optical element includes: a substrate; a protrusion and recess portion that is formed on one surface of the substrate and imposes predetermined diffraction on incident light; and an antireflection layer provided between the substrate and the protrusion and recess portion. An effective refractive index difference Δn in a wavelength range of the incident light between a first medium constituting a protrusion of the protrusion and recess portion and a second medium constituting a recess of the protrusion and recess portion is 0.70 or more. An exit angle range θ out  of diffraction light exiting from the protrusion and recess portion when the incident light enters the substrate from a normal direction of the substrate is 60° or more. Total efficiency of diffraction light exiting from the protrusion and recess portion in the exit angle range is 65% or more.

TECHNICAL FIELD

The present invention relates to a diffractive optical element thatgenerates light spots having a predetermined pattern, and a projectiondevice and a measurement device that are equipped with the diffractiveoptical element.

BACKGROUND ART

There is a device that measures a position, a shape, etc. of ameasurement target object by applying predetermined light to themeasurement target object and detecting light scattered by themeasurement target object (refer to Patent document 1, for example). Inthe kind of measurement device, a diffractive optical element can beused for applying a particular light pattern to a measurement target.

For example, there is a common diffractive optical element that isobtained by forming protrusions and recesses on a substrate surface.Diffractive optical elements having such a protrusion and recessstructure diffract light by giving it a desired difference of opticalpath length utilizing a diffractive index difference between a material(e.g. air having a refractive index of 1) that fills up the recesses anda material of the protrusions.

Another example of common diffractive optical elements has aconfiguration in which recesses are filled up with (more specifically,the recesses are filled up with and the top surfaces of protrusions areformed with) a refractive material which has a different refractiveindex from that of a material of the protrusions and which is not air.Since the surfaces of the protrusions and the recesses are not exposed,this configuration can reduce a variation of diffraction efficiencycaused by adhesion of substances. For example, Patent Literature 2discloses a diffractive optical element in which another transparentmaterial having a different refractive index is provided so as to fillup a protrusion and recess pattern for generating two-dimensional lightspots.

Some optical devices use invisible light such as near infrared light.Examples of them include a remote sensing device that is used for faceauthentication and focusing of a camera device in smartphones etc., aremote sensing device that is connected to a game machine and used fordetecting motion of a user, and a LIDAR (light detecting and ranging)device that is used in vehicles etc. to detect a nearby object.

Some of the above optical devices are required to apply light so thatits emission angle is much different from a traveling direction ofincident light. For example, in, for example, a use of focusing in acamera device that has a wide angle of view used in a smartphone or thelike, and a use of detecting a nearby object such as an obstacle and afinger to be displayed on a display device in a device having a displayscreen suitable for a human viewing angle such as a VR (virtual reality)headset, the application of light in a wide angular range of 60° ormore, 100° or more, or 120° or more may be desired.

To allow light to exit in such a wide angular range utilizing adiffractive optical element, it is necessary to form a protrusion andrecess structure at a small pitch. In particular, in the case of aprotrusion and recess structure that provides a wide exit angle rangefor long-wavelength incident light such as near infrared light, theprotrusions tend to be increased in height to obtain a desireddifference of optical path length. The height of protrusions may read asthe depth of recesses.

In the case where the pitch of the protrusion and recess portion of adiffractive optical element is made small or its height is increased,the aspect ratio (e.g., (height of protrusions)/(width of protrusions))is increased accordingly. In the case where the aspect ratio isincreased, the ratio of the area of the side surfaces (of theprotrusions) of the protrusion and recess portion capable of serving asinterfaces for light traveling through the protrusion and recess portionto the area of all surfaces is increased, which may increase theinfluence of reflection at the side surfaces of protrusions and so onsuch that undesired 0th-order light may be generated. Typically,irradiation of strong 0th-order light is considered to be undesirablefrom the viewpoint of safety of eyes.

As for techniques for reducing 0th-order light in diffractive opticalelements, Patent Literature 3, for example, discloses a configuration inwhich two diffractive optical elements (DOEs) are provided. In thetechnique disclosed in Patent Literature 3, 0th-order light is reducedby a configuration in which 0th-order light generated by a firstdiffractive optical element is diffracted by a second diffractiveoptical element.

CITATION LIST Patent Literature

Patent Literature 1: Japanese Patent No. 5,174,684

Patent Literature 2: Japanese Patent No. 5,760,391

Patent Literature 3: JP-A-2014-209237

SUMMARY OF INVENTION Technical Problems

A method for enabling wide-range irradiation while reducing thegeneration of undesired 0th-order light would be increasing thedifference of refractive index between a material (e.g., air having arefractive index 1) for filling up the recesses and a material of theprotrusions. Since the height of the protrusions can be reduced byincreasing the difference between the refractive indexes, generation ofundesired 0th-order light can be reduced by reducing the influence ofreflection at the side surfaces of the protrusions and so on.

However, the combination of materials that increases the difference ofrefractive index between the protrusions and the recesses has problemsthat the reflectivity is high at the interfaces between these materials(in particular, the material having a high refractive index) and othermedia (e.g., substrate and air) so that the efficiency of lightutilization is lowered or stray light is generated. In the case ofgenerating many light spots or measuring return light (e.g., scatteringlight) of light applied by generated light spots, for example inprojection devices and measurement devices, these problems are notpreferable because they make it difficult to obtain high accuracy.

An object of the present invention is therefore to provide a diffractiveoptical element that is high in the efficiency of light utilization andcan apply light in a wide range while reducing the generation ofundesired 0th-order light, and a projection device and a measurementdevice that are equipped with that diffractive optical element.

Solution to Problem

A diffractive optical element in the present invention, includes: asubstrate; a protrusion and recess portion that is formed on one surfaceof the substrate and imposes predetermined diffraction on incidentlight; and an antireflection layer provided between the substrate andthe protrusion and recess portion, in which: an effective refractiveindex difference Δn in a wavelength range of the incident light betweena first medium constituting a protrusion of the protrusion and recessportion and a second medium constituting a recess of the protrusion andrecess portion is 0.70 or more; an exit angle range θ_(out) ofdiffraction light exiting from the protrusion and recess portion whenthe incident light enters the substrate from a normal direction of thesubstrate is 60° or more; and total efficiency of diffraction lightexiting from the protrusion and recess portion in the exit angle rangewith respect to a quantity of entire light entering the protrusion andrecess portion in the wavelength range of the incident light is 65% ormore.

A projection device in the present invention, includes: a light source;and the diffractive optical element, in which a ratio of a lightquantity of light irradiating a predetermined projection surface to alight quantity of light emitted from the light source is 50% or more.

A measurement device in the present invention, includes: a projectionunit configured to emit inspection light; and a detection unitconfigured to detect scattering light generated as a result ofirradiation of the inspection light emitted from the projection unit toa measurement target object, in which the projection device is providedas the projection unit.

Advantageous Effects of Invention

The invention can provide a diffractive optical element that is high inthe efficiency of light utilization and can apply light in a wide rangewhile reducing the generation of undesired 0th-order light, and aprojection device and a measurement device that are equipped with thatdiffractive optical element.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic sectional view of a diffractive optical element 10according to a first embodiment.

FIG. 2A to FIG. 2C are schematic sectional views showing other examplesof diffractive optical elements 10.

FIG. 3A to FIG. 3C are schematic sectional views showing other examplesof diffractive optical elements 10.

FIG. 4 is an explanatory diagram showing an example of light patterngenerated by the diffractive optical element 10.

FIG. 5A and FIG. 5B are graphs showing a relationship between thegrating depth d and the intensity of 0th-order light (0th-orderefficiency).

FIG. 6 is a graph showing relationships between the diagonal viewingangle θ_(d) and the 0th-order efficiency (minimum value) for fivematerials having different refractive indexes.

FIG. 7A and FIG. 7B are graphs showing a relationship between Δn/NA andthe 0th-order efficiency (minimum value) for each of the five materialshaving different refractive indexes.

FIG. 8 is a schematic sectional view showing another example ofdiffractive optical element 10.

FIG. 9A and FIG. 9B are graphs showing calculation results ofreflectance of diffractive optical elements 10 of Example 1.

FIG. 10 is a graph showing incident angle dependence of the reflectanceof an antireflection layer 14 of Example 1 for light having a wavelengthof 850 nm.

FIG. 11A and FIG. 11B are graphs showing calculation results ofreflectance of an internal antireflection layer 13 of Example 1.

FIG. 12 is a graph showing incident angle dependence of the reflectanceof the internal antireflection layer 13 of Example 1 for light having awavelength of 850 nm.

FIG. 13 is a schematic diagram for illustrating diffraction light thatexits from the diffractive optical element 10.

FIG. 14 is a graph showing calculation results of 0th-order efficiencyof each of Example 1, Example 2, and Comparative Example 1.

FIG. 15 is a graph showing calculation results of total efficiency ofeach of Example 1, Example 2, and Comparative Example 1.

DESCRIPTION OF EMBODIMENTS

Embodiments of the present invention will be hereinafter described withreference to the drawings. FIG. 1 is a schematic sectional view of adiffractive optical element 10 according to a first embodiment. Thediffractive optical element 10 is equipped with a substrate 11, aprotrusion and recess portion 12 formed on one surface of the substrate11, and an antireflection layer 13 provided between the substrate 11 andthe protrusion and recess portion 12. In the following, theantireflection layer 13 which is provided between the substrate 11 andthe protrusion and recess portion 12 will be referred to as an internalantireflection layer 13.

In the case where a light incidence direction is not explicitly shown inthe embodiment, it is assumed that light travels in the +z direction orupward in the figure. The light traveling direction is not limited tothose directions and may be in the −z direction or downward.

The substrate 11 is not particularly limited as long as the substrate 11is a member that is transparent at used wavelength such as glass or aresin. The used wavelength means a wavelength range of light incident onthe diffractive optical element 10. The following description will bemade with an assumption that light in a particular wavelength range(e.g., 850±20 nm) within a wavelength range of visible light and nearinfrared light being 700 nm to 1,200 nm enters the diffractive opticalelement 10. However, the used wavelength is not limited to thewavelength range. In addition, unless otherwise mentioned, it is assumedthat the visible wavelength range is 400 nm to 780 nm, the infraredwavelength range is 780 nm to 2,000 nm (near infrared range; inparticular, 800 nm to 1,000 nm), and the ultraviolet wavelength range is300 nm to 400 nm (near ultraviolet range; in particular 360 nm to 380nm). The term “visible light” means light in the above visible range,the term “infrared light” means light in the above infrared range, andthe term “ultraviolet range” means light in the above ultraviolet range.

The protrusion and recess portion 12 is a protrusion and recessstructure having a protrusion and recess pattern that causes diffractionon incident light. More specifically, the protrusion and recess patternis a two-dimensional pattern in a plan view of steps formed byprotrusions 121 of the protrusion and recess portion 12. The term “planview” used herein means a plan view as viewed from the travelingdirection of light incident on the diffractive optical element 10 andcorresponds to a plan view as viewed from the normal direction of themain surface of the diffractive optical element 10. The protrusion andrecess pattern is formed so that light spots of plural respectivediffraction light beams generated by the protrusion and recess patternhave a predetermined pattern on a predetermined projection surface orthe like.

A protrusion and recess pattern that generates plural light spots tohave a particular light pattern on a predetermined projection surface isobtained by, for example, applying Fourier-transformation to a phasedistribution of light that exits from the protrusion and recess pattern.

In the embodiment, the downward direction is defined as the directionfrom the protrusion and recess portion 12 to the substrate 11 and theupward direction is the direction from the substrate 11 to theprotrusion and recess portion 12. Thus, among the top surfaces of eachstep of the protrusion and recess portion 12, the surface that isclosest to the substrate 11 is the bottommost surface and the surfacethat is most distant from the substrate 11 is the topmost surface.

In the following, in a protrusion and recess pattern (i.e., surfacesformed by the protrusion and recess portion 12 on the surface of thesubstrate 11 and having protrusions and recesses in a cross section) forcausing a phase difference, portions that are located above lowestportions (first step s1 in the figure) will be referred to asprotrusions 121 and portions that are recessed portions surrounded bythe protrusions 121 and located below highest portions (in this example,second step s2) will be referred to as recesses 122. The height ofportions, causing a phase difference actually, of the protrusion andrecess portion 12, more specifically, the distance from the first steps1 of the protrusion and recess pattern to the topmost portions of theprotrusions 121, will be referred to as a height d of the protrusions121 or a grating depth d. Furthermore, in the following, a portion, notcausing a phase difference, of the protrusion and recess portion 12 (inFIG. 1 , the portion made of the same material as the bottommostportions of the protrusions 121, covers the surface of the substrate 11,and constitutes the first step s1) may be referred to as a base portion123 (or underlying layer). The base portion 123 is located between theinternal antireflection layer 13 and the protrusions 121 or recesses122. However, the base portion 123 is not indispensable. That is, thebase portion 123 may be either present or absent.

As for the number of steps of a protrusion and recess pattern, as incommon diffraction gratings, each surface that constitutes steps forgiving a phase difference to incident light is regarded as one step.FIG. 1 shows an example of a diffractive optical element 10 having aprotrusion and recess portion 12 that constitutes a binary diffractiongrating, that is, a two-step protrusion and recess pattern.

FIG. 2A shows another example of diffractive optical elements 10. Asshown in FIG. 2A, a diffractive optical element 10 can be configured insuch a manner that a member other than a member constituting aprotrusion and recess portion 12 (in this example, a member in anoutermost layer of an internal antireflection layer 13, which will bedescribed later) constitutes a first step of a protrusion and recesspattern. Also in this case, the height d of protrusions 121 is definedas the distance from the first step s1 of the protrusion and recesspattern to the topmost portions of the protrusions 121.

The configuration shown in FIG. 1 is a configuration in which the secondmedium (air) that fills up the recesses 122 is not in contact with theinternal antireflection layer 13 at least in an effective regionincident light enters. Alternatively, as shown in FIG. 2A and FIG. 2B, aconfiguration is possible in which the second medium (air) is in contactwith the internal antireflection layer 13 at least in part of aneffective region. In the latter case, the protrusion and recess portion12 does not include a base portion 123. Both of FIG. 2A and FIG. 2B showan example diffractive optical element 10 that is equipped with aprotrusion and recess portion 12 that constitutes a two-step protrusionand recess pattern and does not include a base portion 123. In thiscase, the second medium (air) constituting the recesses 122 is incontact with the internal antireflection layer 13 at least in part of aneffective region.

In the example shown in FIG. 2A, the protrusion and recess portion 12 isformed on a flat internal antireflection layer 13. On the other hand, inthe example shown in FIG. 2B, the protrusion and recess portion 12 isformed on an internal antireflection layer 13 having steps in thesurface. In this case, in terms of function, portions made of the samematerial as a flat internal antireflection layer 13 (more specifically,bottommost layer) of the protrusions 121 may be regarded as being formedon the internal antireflection layer 13.

In this case, the height d of the protrusions 121 is defined so as toinclude the thickness of the portions located at the bottommost layer(see FIG. 2C). In this case, the internal antireflection layer 13 hasdifferent thickness in regions where it is in contact with theprotrusions 121 and in regions where it is in contact with the recesses122. However, there is no problem as long as the internal antireflectionlayer 13 is formed in each region in a configuration in which interfacereflection between the internal antireflection layer 13 and the othermedium in contact with the internal antireflection layer 13 can bereduced. For example, in the configuration shown in FIG. 2C, theinternal antireflection layer 13 may have any configuration as long asinterface reflection between the substrate 11 and the protrusions 121 inthe regions where it is in contact with the protrusions 121 andinterface reflection between the substrate 11 and the recesses 122 inthe regions where it is in contact with the recesses 122 can be reduced.The requirements for the internal antireflection layer 13 are the samealso in the case where the internal antireflection layer 13 has aconstant thickness. For example, in the case where, as shown in FIG. 1 ,the protrusion and recess portion 12 includes the base portion 123, theinternal antireflection layer 13 may have any configuration as long asinterface reflection between the substrate 11 and the base portion 123that are in contact with the internal antireflection layer 13. On theother hand, in the case where the internal antireflection layer 13 hasdifferent thickness in regions where it is in contact with theprotrusions 121 and in regions where it is in contact with the recesses122, if the difference is smaller than or equal to 2% of the height d ofthe protrusions 121, the portions, constituting the bottommost layer ofthe protrusions 121, of the internal antireflection layer 13 are notregarded as parts of the protrusions 121.

On the other hand, in the case where the portions (denoted by a in FIG.2C) contributes to production of a phase difference by the protrusionand recess portion 12, a height and a refractive index (in this case,effective refractive index) of the protrusions 121 may be determined byregarding a part located above lowest portions (in a sense that theportions concerned are included) in the protrusion and recess pattern asthe protrusions 121, according to the above-mentioned definition.

The material of the protrusion and recess portion 12 has a refractiveindex at used wavelength of 1.70 or more. Examples of such a materialinclude inorganic materials that are oxides, nitrides, and oxynitridesof Zn, Al, Y, In, Cr, Si, Zr, Ce, Ta, W, Ti, Nd, Hf, Mg, La, Nb, and Bi,fluorides of Al, Y, Ce, Ca, Na, Nd, Ba, Mg, La, and Li, and siliconcarbide and mixtures thereof. Transparent conductors such as ITO canalso be used. Other examples thereof include Si, Ge, diamond-likecarbon, and materials obtained by adding an impurity such as hydrogen tothese materials. The material of the protrusion and recess portion 12 isnot limited to inorganic materials as long as the refractive index atused wavelength satisfy the above-mentioned condition. Examples ofmaterials that contain an organic material and have a refractive indexof 1.70 or more include a thiourethane-based resin, an episulfide resin,polyimide, and what is called a nanocomposite material obtained bydispersing fine particles of an inorganic material in an organicmaterial. Examples of fine particles of an inorganic material includeoxides of Zr, Ti, Al, etc.

In the case where the recesses 122 are filled up with a medium otherthan air, the refractive index difference Δn between the protrusions 121and the recesses 122 at used wavelength should be 0.70 or more. However,from the viewpoints of material selectivity and thinning, it ispreferable that the recesses 122 be filled up with air.

As shown in FIG. 3A to FIG. 3C, the protrusions 121 of the protrusionand recess portion 12 may have a multilayer structure. FIG. 3A shows anexample in which each protrusion 121 is a multilayer film of two layers.FIG. 3B shows an example in which each protrusion 121 is a multilayerfilm of four layers. Although in the examples shown in FIG. 3A and FIG.3B the protrusion and recess portion 12 does not include a base portion123, as shown in FIG. 3C the protrusion and recess portion 12 may beformed so as to include a base portion 123 and at least each protrusion121 is a multilayer film. In this case, the bottommost layer of eachprotrusion 121 and the base portion 123 may either be made of the samematerial or not.

As shown in FIG. 3A to FIG. 3C, it is more preferable that eachprotrusion 121 have a multilayer structure and its topmost layer 121 thaving a surface that is in contact with the air be made of alow-refractive index material whose refractive index is relatively lowamong the materials contained in the protrusion 121. For example, eachprotrusion 121 may be formed using, as a material, a multilayer film inwhich a low-refractive index material and a high-refractive indexmaterial are alternately layered. In this case, the total reflectancecan be lowered further because, in addition to an effect of reducing thereflectance at the interfaces between the substrate 11 and theprotrusion and recess portion 12 obtained by the internal antireflectionlayer 13, the reflectance at the interfaces between the protrusions 121and the air can be reduced by forming the topmost layer 121 t of eachprotrusion 121 using the low-refractive index material. The efficiencyof light utilization can thus be increased further.

In the case where each protrusion 121 has a multilayer structure, theabove-mentioned term “refractive index difference Δn” may read as adifference in terms of an effective refractive index ns described below(hereinafter referred to as an “effective refractive index difference”).In the embodiments, the effective refractive index difference of eachprotrusion 121 having a multilayer structure is defined as follows.

That is, the refractive index and the thickness of each layer(hereinafter referred to as a “grating layer”) of the multilayer filmconstituting each protrusion 121 is respectively denoted by ns_(r) andds_(r), and the effective refractive index given by the followingformula (1) is denoted by ns, where r is the identifier of each gratinglayer and is an integer from 1 to the number layers. The denominatorΣ_(r)(ds_(r)) is the sum of each of the thickness of grating layers,which corresponds to the height d of each protrusion 121.(Effective refractive index ns)=Σ_(r)(ns _(r) ×ds _(r))/Σ_(r)(ds_(r))  (1)

Since a refractive index of each protrusion 121 having a single layerstructure can also be calculated according to formula (1) by setting rto be 1, the “refractive index difference Δn” of the protrusion andrecess portion 12 can read as the “effective refractive index differenceΔn” without discriminating between single layer protrusions 121 andmultilayer protrusions 121.

The number of materials of the multilayer film of each protrusion 121 isnot limited to two. For example, each protrusion 121 may be formed by amultilayer film made of one or more materials whose refractive indexesare higher than the effective refractive index of the protrusion 121 andone or more materials whose refractive indexes are lower than theeffective refractive index of the protrusion 121. In this case, thetopmost layer 121 t of each protrusion 121 should be made of a materialwhose refractive index is lower than the effective refractive index ofthe protrusion 121. In the following, in the multilayer filmconstituting each protrusion 121, the material whose refractive index islower than the effective refractive index of the protrusion 121 may bereferred to as a low-refractive index material and the material whoserefractive index is higher than the effective refractive index of theprotrusion 121 may be referred to as a high-refractive index material.

Next, the diffraction caused by the diffractive optical element 10 willbe described using an example light pattern that is generated by adiffractive optical element 10 shown in FIG. 4 . The diffractive opticalelement 10 is formed so that a diffraction light beam group 22 thatexits correspondingly to an incident light beam 21 with the optical axisdirection extending in the Z axis is distributed two-dimensionally. Withthe diffractive optical element 10, a group of light beams isdistributed in an angular range from a minimum angle θx_(min) (notshown) to a maximum angle θx_(max) (not shown) on the X axis and in anangular range from a minimum angle θy_(min) (not shown) to a maximumangle θy_(max) (not shown) on the Y axis, where the X axis is defined asan axis that intersects the Z axis and is perpendicular to the Z axisand the Y axis is defined as an axis that is perpendicular to both ofthe X axis and the Z axis.

The X axis and Y axis are approximately parallel with the longer sidesand the shorter sides of a light spot pattern, respectively. A range ofirradiation with the diffraction light beam group 22 that is from theminimum angle θx_(min) to the maximum angle θx_(max) in the X-axisdirection and in a range from the minimum angle θy_(min) to the maximumangle θy_(max) in the Y-axis direction approximately coincides with alight detection range of a photodetecting element used together with thediffractive optical element 10. In the light spot pattern of thisexample, straight lines each of which is parallel with the Y axis andpasses through a light spot at which the angle in the X direction withrespect to the Z axis is θx_(max) are the above-mentioned shorter sidesand straight lines each of which is parallel with the X axis and passesthrough a light spot at which the angle θy_(max) in the Y direction withrespect to the Z axis are the above-mentioned longer sides. In thefollowing, the angle at the diffractive optical element 10 subtended bya diagonal line connecting the intersection of a shorter side and alonger side and another intersection diagonal to the former is denotedby θ_(d) and is referred to as a “diagonal angle.” The diagonal angleθ_(d) (hereinafter referred to as a “diagonal viewing angle θ_(d)”) isset equal to an exit angle range θ_(out) of the diffractive opticalelement 10. The exit angle range θ_(out) is an angular range indicatingan expanse of a light pattern that is formed by diffraction light thatexits from the protrusion and recess portion 12 when incident lightenters the substrate 11 from its normal direction. Instead of being setequal to the diagonal viewing angle θ_(d), the exit angle range θ_(out)of the diffractive optical element 10 may be set equal to, for example,a maximum value of an angle formed by two light beams included in thediffraction light beam group 22.

In the diffractive optical element 10, for example, the exit angle rangeθ_(out) when incident light enters the substrate 11 from the directionthat is normal to its surface should be 60° or more, preferably 70° ormore. For example, some camera devices installed in smartphones etc.have angles of view (full angles) being about 50° to 90°. Some LIDARdevices used for autonomous driving etc. have angles of view being about30° to 70°. Furthermore, the human viewing angle is typically about120°, and camera devices of VR headsets having angles of view 70° to140° are realized. To apply the diffractive optical element 10 to thosedevices, the exit angle range θ_(out) of the diffractive optical element10 may be set 100° or more, or 120° or more.

The number of light spots generated by the diffractive optical element10 may be 4 or more, 9 or more, 100 or more, or 10,000 or more. Althoughthere are no particular limitations on the upper limit of the number oflight spots, the upper limit may be 10,000,000, for example.

In FIG. 4 , symbol R_(ij) denotes divisional regions of the projectionsurface. For example, the diffractive optical element 10 may beconfigured so that where the projection surface is divided into theplural regions R_(ij) a distribution density of light spots 23 of thelight beam group 22 irradiating each region R_(ij) is within ±50% of anaverage value over all of the regions. The distribution density may bewithin ±25% of an average value over all the regions. This configurationis suitable for a measurement purpose etc. because the distribution oflight spots 23 in the projection surface can be made uniform. Here, theprojection surface may be not only a flat surface but also a curvedsurface. Where the projection surface is a flat surface, it is notlimited to a surface that is perpendicular to the optical axis of theoptical system and may be a surface that is inclined with respect to theoptical axis.

Each diffraction light beam included in the diffraction light beam group22 shown in FIG. 4 is light that has been diffracted by an angle θ_(x0)in the X direction and an angle θ_(y0) in the Y direction with respectto the Z-axis direction as given by grating equations (2). In Equations(2), m_(x) is the order of diffraction in the X direction, m_(y) is theorder of diffraction in the Y direction, λ is the wavelength of a lightbeam 21, P_(x) and P_(y) are the pitches of the diffractive opticalelement in the X-axis direction and the Y-axis direction, respectively,and θ_(xi) and θ_(yi) are incident angles to the diffractive opticalelement in the X-axis direction and the Y-axis direction, respectively.When the diffraction light beam group 22 irradiates the projectionsurface of a screen, a measurement target object, or the like, plurallight spots 23 are formed in an irradiated area.sin θ_(xo)=sin θ_(xi) +m _(x) λ/P _(x)sin θ_(yo)=sin θ_(yi) +m _(y) λ/P _(y)   (2)

In the case where the protrusion and recess portion 12 has stepwisequasi-blazed shape having N steps, it is preferable that Δnd/λ=(N−1)/Nbe satisfied because a wavefront in which an optical path lengthdifference produced by the protrusion and recess portion 12 correspondsto one wavelength can be approximated, thereby achieving highdiffraction efficiency. For example, in an example case that nearinfrared light enters a protrusion and recess pattern that is formed byprotrusions 121 made of a material having a refractive index of 1.7 andrecesses 122 constituted by air, the above relationship is0.7d/λ=(N−1)/N. Thus, the height d of the protrusions 121 preferablysatisfies d={(N−1)/N}×λ/0.7.

FIG. 5A and FIG. 5B are graphs showing relationships between the height(grating depth) d of the protrusions 121 and the intensity of 0th-orderlight (0th-order efficiency). Here, the 0th-order efficiency indicatingthe intensity of 0th-order light means the ratio of a light quantity oftransmission 0th-order light that exits from the protrusion and recessportion 12 with respect to the quantity of entire light entering theprotrusion and recess portion 12. FIG. 5A is a graph showing arelationship between the grating depth and the intensity of 0th-orderlight in the case where the grating depth is in a range of 0.05λ to2.0λ, and FIG. 5B is a graph that is an enlarged view of a part of FIG.5A. FIG. 5A and FIG. 5B show design examples of cases that 441 lightspots in total (21 points in the X direction and 21 points in the Ydirection) are formed in a range in which a diagonal numerical apertureNA is 0.85 (NAs in the X direction and the Y direction are 0.6) andsynthesized quartz (refractive index n: 1.45) or Ta₂O₅ (n: 2.1) is usedas a material of the protrusions 121. In the embodiment, NA is an indexthat is given by 1·sin(θ_(out)/2).

As shown in FIG. 5A and FIG. 5B, in the case where the refractive indexis 1.45, in design, the configuration that realizes the NA of 0.85 (exitangle range θ_(out): about 116°) cannot make the 0th-order efficiencylower than 5% no matter how the height d of the protrusions 121 isadjusted. On the other hand, in the case where the refractive index is2.1, the 0th-order efficiency can be made, for example, 1% or less byadjusting the height d of the protrusions 121.

In connection with the above, to lower the 0th-order efficiency whileobtaining high diffraction efficiency for diffraction light of designorders other than the 0th order, a relationship of Δn/NA≥0.7 ispreferably satisfied. Incidentally, Δn/NA is preferably 0.7 or more,more preferably 1.0 or more. FIG. 6 is a graph showing relationshipsbetween the diagonal viewing angle θ_(d) and the 0th-order efficiency(minimum value) in cases where five materials having differentrefractive indexes are used as the material of the protrusions 121.

The five materials having different refractive indexes have refractiveindexes of 1.45 (synthesized quartz), 1.60 (polycarbonate-based resin),1.70 (SiON), 1.90 (HfO), and 2.10 (Ta₂O₅), respectively. FIG. 6 shows0th-order efficiency (minimum values) calculated by a rigorouscoupled-wave analysis (RCWA) for design solutions obtained for diagonalviewing angles θ_(d) of 50.2°, 68.8°, 90.0°, 116.0°, 133.4°, and 163.4°,respectively. FIG. 6 shows that the 0th-order efficiency lowers as therefractive index of the protrusions 121 increases. NAs corresponding tothe above-mentioned diagonal viewing angles θ_(d) are 0.424, 0.565,0.707, 0.848, 0.918, and 0.989, respectively.

FIG. 7A and FIG. 7B shows a relationship between Δn/NA and the 0th-orderefficiency (minimum value) in each of the above-mentioned designsolutions. FIG. 7A is a graph showing a full relationship of each of theabove-mentioned design solutions, and FIG. 7B is a graph that is anenlarged view of a part of FIG. 7A.

In each of the above examples, the design wavelength is set at 850 nmand the recesses are assumed to be air (n=1). The protrusion and recessportion 12 has an 8-step protrusion and recess pattern that produces 441light spots (21 points in the X direction and 21 points in the Ydirection), and gratings of the protrusion and recess pattern areregularly arranged, and all separation angles of adjacent light spotsare the same. Table 1 shows design parameter of each example.

TABLE 1 Refractive index 0th-order Protrusions Exit angle (full angle)(deg) d efficiency No. (n) X direction Y direction Diagonal NA Δnd/λ(μm) (%) 1 1 1.45 34.9 34.9 50.2 0.424 1.15 2.17 0.30 2 1.45 47.1 47.168.8 0.565 1.15 2.17 1.22 3 1.45 60.0 60.0 90.0 0.707 1.20 2.27 2.94 41.45 73.7 73.7 116.0 0.848 1.20 2.27 5.44 5 1.45 81.0 81.0 133.4 0.9181.20 2.27 7.26 6 1.45 88.8 88.8 163.4 0.989 1.20 2.27 9.60 2 1 1.60 34.934.9 50.2 0.424 1.15 1.63 0.12 2 1.60 47.1 47.1 68.8 0.565 1.15 1.630.44 3 1.60 60.0 60.0 90.0 0.707 1.15 1.63 1.37 4 1.60 73.7 73.7 116.00.848 1.20 1.70 2.74 5 1.60 81.0 81.0 133.4 0.918 1.20 1.70 3.63 6 1.6088.8 88.8 163.4 0.989 1.20 1.70 4.67 3 1 1.70 34.9 34.9 50.2 0.424 1.151.40 0.07 2 1.70 47.1 47.1 68.8 0.565 1.15 1.40 0.18 3 1.70 60.0 60.090.0 0.707 1.15 1.40 0.77 4 1.70 73.7 73.7 116.0 0.848 1.15 1.40 1.71 51.70 81.0 81.0 133.4 0.918 1.20 1.46 2.37 6 1.70 88.8 88.8 163.4 0.9891.20 1.46 3.00 4 1 1.90 34.9 34.9 50.2 0.424 1.10 1.04 0.15 2 1.90 47.147.1 68.8 0.565 1.10 1.04 0.07 3 1.90 60.0 60.0 90.0 0.707 1.15 1.090.12 4 1.90 73.7 73.7 116.0 0.848 1.15 1.09 0.43 5 1.90 81.0 81.0 133.40.918 1.15 1.09 0.79 6 1.90 88.8 88.8 163.4 0.989 1.20 1.13 1.15 5 12.10 34.9 34.9 50.2 0.424 1.10 0.85 0.14 2 2.10 47.1 47.1 68.8 0.5651.10 0.85 0.06 3 2.10 60.0 60.0 90.0 0.707 1.15 0.89 0.15 4 2.10 73.773.7 116.0 0.848 1.15 0.89 0.28 5 2.10 81.0 81.0 133.4 0.918 1.15 0.890.47 6 2.10 88.8 88.8 163.4 0.989 1.15 0.89 0.72

As shown in FIG. 7A and FIG. 7B, as for the relationship between the0th-order efficiency and Δn/NA, in the case where, for example, Δn/NA is0.7 or more, the minimum value of the 0th-order efficiency can be madesmaller than 3.0% in all of design solutions in which the exit anglerange θ_(out) is 70° or more (smaller than 165°). For example, in thecase where Δn/NA is 0.9 or more, the minimum value of the 0th-orderefficiency can be made smaller than 1.5% in many of design solutions inwhich the exit angle range θ_(out) is larger than or equal to 100°(smaller than 165°). For another example, in the case where Δn/NA is 1.0or more, the minimum value of the 0th-order efficiency can be madesmaller than 1.0% in many of design solutions in which the exit anglerange θ_(out) is smaller than 165°. For a further example, where Δn/NAis 1.2 or more, the minimum value of the 0th-order efficiency can bemade smaller than 0.5% in many of design solutions in which the exitangle range θ_(out) is smaller than 140°. Among the design solutionsshown in FIG. 5A to FIG. 7B, the ones in which n is 1.45 or 1.60 arecomparative examples. In the diffractive optical element 10 according tothe embodiment, it is preferable that the 0th-order efficiency (theratio of a light quantity of 0th-order transmission light with respectto an incident light quantity) which is diffraction efficiency of0th-order transmission light that exits from the diffractive opticalelement 10 when incident light enters the diffractive optical element 10vertically (from the normal direction of the substrate 11) be lower than3.0%, even preferably lower than 1.5%, further preferably lower than1.0%, particularly preferably lower than 0.5%, and most preferably lowerthan 0.3%.

The internal antireflection layer 13 is provided to prevent reflectionat the interface between the substrate 11 and the protrusion and recessportion 12. There are no particular limitations on the internalantireflection layer 13 except that the internal antireflection layer 13should have an antireflection function for lowering the reflectance ofat least light having the design wavelength at the interface between thesubstrate 11 and the protrusion and recess portion 12. Examples of theinternal antireflection layer 13 include a thin film having a singlelayer structure and multilayer films such as a dielectric multilayerfilm.

For example, in the case where the internal antireflection layer 13 is asingle-layer thin film, it is even preferable that it satisfy thefollowing condition relationship (3). In relationship (3), n_(r) andd_(r) are the refractive index and the thickness of the material of theinternal antireflection layer, respectively, n_(m) is the refractiveindex of the medium that shares the incidence-side interface with theinternal antireflection layer, and no is the refractive index of themedium that forms the exit side interface with the internalantireflection layer. Due to the feature, the reflectance at theinterfaces can be reduced. Here, in relationship (3), α and β are 0.25and 0.6, respectively. In the following, the condition relationship (3)may be referred to as a “first refractive index relationship relating toa single-layer thin film.” It is even preferable that a be 0.2, furtherpreferably 0.1. It is even preferable that β be 0.4.(n ₀ ×n _(m))^(0.5) −α<n _(r)<(n ₀ ×n _(m))^(0.5)+α; and(1−β)×λ/4<n _(r) ×d _(r)<(1+β)×λ/4   (3)

In the case where the internal antireflection layer 13 is a multilayerfilm, the reflectance R that is given by the following formula (4) ispreferably lower than 1%, even preferably 0.5% or less, for light havingthe design wavelength.

For the internal antireflection layer 13 being a multilayer film, it isassumed that light enters the multilayer film at an incident angle θ₀from a medium M1 that is located on the incidence side of the multilayerfilm and has a refractive index n₀, then passes through a q-layermultilayer film M2 in which each layer has a refractive index n_(r) anda thickness d_(r), and enters a medium M3 that is located on the exitside of the multilayer film and has a refractive index n_(m). In thiscase, a reflectance can be calculated according to formula (4), whereη₀, η_(m), and η_(r) are the effective refractive indexes of the mediaM1, M2, and M3, respectively, in which oblique incidence is taken intoconsideration.

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 1} \right\rbrack & \; \\{{R = {\left( \frac{\eta_{0} - Y}{\eta_{0} + Y} \right)\left( \frac{\eta_{0} - Y}{\eta_{0} + Y} \right)^{*}}}{{{where}\begin{pmatrix}B \\C\end{pmatrix}} = {\left\{ {\prod\limits_{r = 1}^{q}\begin{bmatrix}{\cos\mspace{11mu}\delta_{r}} & {\left( {i\mspace{11mu}\sin\mspace{11mu}\delta_{r}} \right)/\eta_{r}} \\{i\;\eta_{r}\mspace{11mu}\sin\mspace{11mu}\delta_{r}} & {\cos\mspace{11mu}\delta_{r}}\end{bmatrix}} \right\}\begin{bmatrix}1 \\\eta_{m}\end{bmatrix}}}{Y = {C/B}}{{\eta_{0} = {\frac{n_{0}}{\cos\;\theta_{0}}\left( {p\text{-}{polarized}\mspace{14mu}{light}} \right)}},{\eta_{0} = {n_{0}*\cos\;{\theta_{0}\left( {s\text{-}{polarized}\mspace{14mu}{light}} \right)}}}}{{\eta_{m} = {\frac{n_{m}}{\cos\;\theta_{m}}\left( {p\text{-}{polarized}\mspace{14mu}{light}} \right)}},{\eta_{m} = {n_{m}*\cos\;{\theta_{m}\left( {s\text{-}{polarized}\mspace{14mu}{light}} \right)}}}}{{\eta_{r} = {\frac{n_{r}}{\cos\;\theta_{r}}\left( {p\text{-}{polarized}\mspace{14mu}{light}} \right)}},{\eta_{r} = {n_{r}*\cos\;{\theta_{r}\left( {s\text{-}{polarized}\mspace{14mu}{light}} \right)}}}}{\delta_{r} = {2\pi\; n_{r}d_{r}\mspace{11mu}\cos\mspace{11mu}{\theta_{r}/\lambda}}}{{n_{0}*\sin\mspace{11mu}\theta_{o}} = {{n_{m}*\sin\mspace{11mu}\theta_{m}} = {n_{r}*\sin\mspace{11mu}\theta_{r}}}}} & (4)\end{matrix}$

Thus, in the case where the internal antireflection layer 13 is notformed, Y is equal to η_(m) and relatively strong reflection occurs. Incontrast, the reflection can be reduced in the case where Y is madecloser η₀ by the internal antireflection layer 13. In particular, in thecase of perpendicular incidence, η₀, η_(m), and η_(r) are equivalent torefractive indexes. In the following, the reflectance R that is given byformula (4) may be referred to as a “theoretical reflectance of amultilayer structure.”

Although the member that constitutes the protrusions 121 of theprotrusion and recess portion 12 is typically a thin film and acalculation needs to be performed by regarding it as part of amultilayer film as described above, in the case where the internalantireflection layer 13 is formed as described above, the reflectancecan be lowered without dependence on the thickness of the thin filmconstituting the protrusions 121 of the protrusion and recess portion12. An interference effect may be taken into consideration by applyingformula (4) in which q=1 to a single-layer internal antireflection layer13.

In the case where light (wavelength: λ (nm)) enters the internalantireflection layer 13 obliquely, it is preferable that the followingcondition be satisfied for perpendicular light incidence. That is, it ispreferable that a local minimum value of a transmittance spectrum in arange of λ−200 nm to λ+200 nm exist in a range of λ to λ+200 nm. It iseven preferable that a local minimum value exist in a range of λ toλ+100 nm. This is because in the case of oblique light incidence, thetransmittance spectrum is shifted to the shorter wavelength side. In theabove configuration, transmittance reduction at the interfaces of theinternal antireflection layer 13 due to oblique incidence can beprevented. Incidentally, λ corresponds to “design wavelength.”

As shown in FIG. 8 , the diffractive optical element 10 may further beprovided with an antireflection layer 14 on the surface of the substrate11 opposite to its surface on which the protrusion and recess portion 12is formed.

The antireflection layer 14 is provided to prevent reflection at theexit side interface of the diffractive optical element 10. There are noparticular limitations on the antireflection layer 14 except that theantireflection layer 14 should have an antireflection function forlowering the reflectance of at least light having the design wavelengthat the exit side interface of the diffractive optical element 10.Examples of the antireflection layer 14 include a thin film having asingle-layer structure or multilayer films such as a dielectricmultilayer film. The conditions related to reflectance for the internalantireflection layer 13 may be employed as they are as conditionsrelated to reflectance for the antireflection layer 14.

In the case where light enters the diffractive optical element 10 fromthe side where the protrusion and recess portion 12 is provided (i.e.,from the −z direction shown in figures), the internal antireflectionlayer 13 and the antireflection layer 14 preferably satisfy theabove-described conditions related to reflectance for light having thedesign wavelength entering at an angle within θ_(out)/2 with respect tothe normal direction of the substrate 11. In the configuration, lightdiffracted by the protrusion and recess portion 12 enters the internalantireflection layer 13 and the antireflection layer 14. The internalantireflection layer 13 and the antireflection layer 14 may satisfy theabove-described reflectance-related conditions for light being aparticular polarization component having the design wavelength thatenters at an angle within θ_(out)/2 with respect to the normal directionof the substrate 11.

For example, the internal antireflection layer 13 and the antireflectionlayer 14 are formed so that the reflectance for at least light havingthe design wavelength and a particular polarization that enters at 40°or less with respect to the normal direction of the substrate 11 is 0.5%or lower. The internal antireflection layer 13 and the antireflectionlayer 14 may be formed so that the reflectance for at least particularpolarized light in the wavelength range of incident light, exiting fromthe diffractive optical element 10 at an angle being ¼ of an exit anglerange θ_(out), that is, ½ of a maximum exit angle (half angle), is 0.5%or less.

The internal antireflection layer 13 and the antireflection layer 14 mayhave, in addition to the antireflection function for light having thedesign wavelength, an antireflection function for light in a particularwavelength range excluding the design wavelength (e.g., ultravioletlight). In devices etc. to be provided with the diffractive opticalelement 10 may be equipped with an optical element other than thediffractive optical element 10. In the above configuration, thediffractive optical element 10 does not interrupt light to be used bysuch an optical element.

In this case, the internal antireflection layer 13 and theantireflection layer 14 may be formed so as to satisfy, in addition tothe above-described conditions for light having the design wavelength, acondition that the reflectance for at least light having a wavelength of360 nm to 370 nm and a particular polarization that enters at 20° orless with respect to the normal direction of the substrate 11 is 1.0% orlower.

The above-mentioned term “reflectance” may read as a reflectance for0th-order light when light going straight (i.e., light traveling in thenormal direction of the substrate 11) enters. In this case, thisreflectance may be determined for each optical path (e.g., for anoptical path passing through a protrusion and for an optical pathpassing through a recess) and for each interface with another medium. Inthis case, in the case where the protrusions 121 or a reflection layerhas a multilayer film structure, a reflectance at the interface with thesubstrate 11 or the air may be determined regarding the multilayer filmstructure for such a desired function as one medium. In the embodiment,it is even preferable that, for example, the sum (total reflectance) ofreflectances at the interfaces between the protrusion and recess portion12 and the other media (substrate 11 and the air) satisfy theabove-described conditions. Such a reflectance can be determined from adifference between a light quantity of straight light entering theprotrusion and recess portion 12 from the side of the substrate 11 and alight quantity of straight light exiting the protrusion and recessportion 12 to the air layer.

In the above, a light quantity of transmission 0th-order light iscalculated by RCWA. However, a light quantity of transmission 0th-orderlight can also be evaluated by causing collimated laser light having thedesign wavelength to enter the diffractive optical element 10 andmeasuring a light quantity of straight transmission light.

In each embodiment described above, there are no particular limitationson the wavelength of incident light. For example, the incident light maybe infrared light (more specifically, light in a wavelength range of 780nm to 1,020 nm). The diffractive optical element according to eachembodiment is more effective in the case of handling light in longerwavelength range than visible light because the protrusions and recessesparticularly tend to be increased in height to elongate the optical pathlength difference.

Since the diffractive optical element according to each embodiment iscapable of diffusing light efficiently, the diffractive optical elementcan be used in projection devices such as a projector. The diffractiveoptical element according to each embodiment can be used as a diffusingelement that is disposed between a light source and a predeterminedprojection surface and serves to project light emitted from the lightsource onto the predetermined projection surface. The diffractiveoptical element according to each embodiment can also be used in a lightprojection device that is included in a device for detecting lightscattered by a target object irradiated with light such as athree-dimensional measurement device or an authentication device andserves to apply inspection light to a predetermined projection area.Furthermore, the diffractive optical element according to eachembodiment can also be used in an intermediate screen (an opticalelement for generating an intermediate image) of a projection devicesuch as a head-up display. In this case, for example, the diffractiveoptical element can also be used as an intermediate screen that isdisposed between a light source for emitting light for forming anintermediate image and a combiner in the projection device and serves toproject, onto the combiner, light emitted from the light source to forman intermediate image.

In each of the above devices, it is preferable that the ratio of thequantity of light irradiating the predetermined projection surface withrespect to the quantity of light that is emitted from the light sourceis 50% or more, by virtue of the effect that the reflectance is loweredin the diffractive optical element. It is even preferable that the ratio(corresponding to a term “total efficiency” described later) of thequantity of diffraction light of a design order irradiating thepredetermined projection surface with respect to the quantity of lightthat is emitted from the light source is 65% or more, further preferably70% or more.

EXAMPLES Example 1

This Example is a diffractive optical element 10 having a protrusion andrecess portion 12 having a multilayer structure that constitutes atwo-step protrusion and recess pattern and includes a base portion 123,like the example diffractive optical element 10 shown in FIG. 3C.However, in this Example, as shown in FIG. 8 , an antireflection layer14 is further provided on the surface of a substrate 11 opposite to itssurface on which the protrusion and recess portion 12 is formed. Thedesign wavelength is 850 nm and the recesses 122 are air (n=1).

In the diffractive optical element 10 of this Example, protrusion andrecess patterns were designed so that the exit angle range θ_(out) (morespecifically, diagonal viewing angle θ_(d)) of a diffraction light groupthat exits the protrusion and recess portion 12 became equal to 50°,68°, 90°, 102°, 116°, 134°, and 164°, respectively. The Examples whoseθ_(d) is 50°, 68°, 90°, 102°, 116°, 134°, and 164° are Examples 1A, 1B,1C, 1D, 1E, 1F, and 1G, respectively. However, Examples 1F and 1G areReferential Examples. In each Example, it was assumed that the gratingof the protrusion and recess pattern was regularly arranged, and allpairs of adjacent light spots had the same separation angle.

In this Example, the material of the substrate 11 was a glass substratehaving a refractive index of 1.514. The material of the protrusion andrecess portion 12 was a two-layer multilayer film made of Ta₂O₅ having arefractive index of 2.192 and SiO₂ having a refractive index of 1.463.The material of the internal antireflection layer 13 was a four-layerdielectric multilayer film made of similar SiO₂ and Ta₂O₅. The materialof the antireflection layer 14 was a six-layer dielectric multilayerfilm made of similar SiO₂ and Ta₂O₅. Table 2 shows specificconfigurations of Examples 1A to 1G of the diffractive optical element10 of this Example. As shown in Table 2, in this Example, Examples 1A to1G are the same in configuration except the structure of the protrusions121.

TABLE 2 Thickness (nm) Refractive Example 1 Configuration Material(s)index A B C D E F G Antireflection SiO₂ 1.463 172 layer Ta₂O₅ 2.192 67SiO₂ 1.463 42 Ta₂O₅ 2.192 18 SiO₂ 1.463 35 Ta₂O₅ 2.192 18 SubstrateBorosilicate 1.514 — glass Internal Ta₂O₅ 2.192 19 antireflection SiO₂1.463 34 layer Ta₂O₅ 2.192 25 SiO₂ 1.463 26 Protrusion Base portionTa₂O₅ 2.192 200 and recess Protrusions 348 354 354 354 361 361 361portion SiO₂ 1.463 146 146 146 146 146 146 146

A manufacturing method of this Example is as follows. First, anantireflection layer 14 that is a six-layer dielectric multilayer filmmade of SiO₂ and Ta₂O₅ is formed on a glass substrate. The material andthickness of each layer are as shown in Table 2.

Then an internal antireflection layer 13 that is a four-layer dielectricmultilayer film made of SiO₂ and Ta₂O₅ is formed on the surface of theglass substrate opposite to its surface on which the antireflectionlayer 14 has been formed. The material and thickness of each layer areas shown in Table 2. Then a two-layer dielectric multilayer film made ofSiO₂ and Ta₂O₅ is formed at a predetermined film thickness as materialsof a protrusion and recess portion 12 including a base portion 123. Forexample, in Example 1A, a Ta₂O₅ film having a film thickness of 548 nmis formed to be a bottommost layer of the base portion 123 and a gratinglayer of the protrusions 121 and an SiO₂ film having a film thickness146 nm to be a topmost layer of the grating layer of the protrusions 121are formed on the Ta₂O₅ film.

Subsequently, the thus-formed two-layer multilayer film made of SiO₂ andTa₂O₅ are processed into a two-step protrusion and recess structure byphotolithography and etching. The heights (grating depths) of theprotrusions 121 of the respective Examples are 494 nm to 507 nm (thesums of the thicknesses of the protrusion materials shown in Table 2). Aheight d (film thickness) of the protrusions 121 can be measured byobservation of a cross section using a step gauge or an SEM (scanningelectron microscope). In this manner, diffractive optical elements 10 ofExamples 1A-1G are obtained.

FIG. 9A and FIG. 9B show calculation results of reflectance of theantireflection layer 14 of this Example. FIG. 9A shows calculationresults of reflectance in a wavelength range of 350 nm to 950 nm, andFIG. 9B shows calculation results of reflectance in part of the abovewavelength range, that is, 800 nm to 900 nm. FIG. 9A and FIG. 9B showcalculation results of cases where the incident angle, that is, theangle of incident light with respect to the normal direction of thesubstrate 11, is 0°, 20°, and 40°. In the case of oblique incidence,calculations were made for p-polarized light and s-polarized light.

FIG. 10 shows incident angle dependence of the reflectance of theantireflection layer 14 of this Example for light having a wavelength of850 nm. As shown in FIG. 10 , the antireflection layer 14 of thisExample realizes reflectance of lower than 2.5% for light (both ofp-polarized light and s-polarized light) having a wavelength of 850 nmand an incident angle of 55° or less. Furthermore, the antireflectionlayer 14 of this Example realizes reflectance that is lower than 1.0%for p-polarized light having a wavelength 850 nm and an incident angleof 45° or less.

FIG. 11A and FIG. 11B show calculation results of reflectance of theinternal antireflection layer 13 of this Example. FIG. 11A showscalculation results of reflectance in a wavelength range of 350 nm to950 nm, and FIG. 11B shows calculation results of reflectance in part ofthe above wavelength range, that is, 800 nm to 900 nm. FIG. 11A and FIG.11B show calculation results of cases where the incident angle, that is,the angle of incident light with respect to the normal direction of thesubstrate 11, is 0°, 20°, and 30°. In the case of oblique incidence,calculations were made for p-polarized light and s-polarized light.

FIG. 12 shows incident angle dependence of the reflectance of theinternal antireflection layer 13 of this Example for light having awavelength of 850 nm. As shown in FIG. 12 , the internal antireflectionlayer 13 of this Example realizes reflectance of lower than 2.5% forlight (both of p-polarized light and s-polarized light) having awavelength of 850 nm and an incident angle of 35° or less. Furthermore,the antireflection layer 14 of this Example realizes reflectance oflower than 0.1% for p-polarized light having a wavelength of 850 nm andan incident angle of 35° or less. Although reflectance of the internalantireflection layer 13 and the antireflection layer 14 for incidentangles of 35° or more are omitted, they can be calculated according tothe above formula (4) using effective refractive indexes of therespective media corresponding to each incident angle.

Table 3 shows detailed data of optical characteristics of Examples1A-1G. Table 3 shows fields of view (°) corresponding to exit angleranges in the X direction, Y direction, and diagonal direction ofexiting light, NAs, a grating depth (nm) of the protrusions 121, aneffective refractive index of the materials of the protrusions 121,total efficiency (%), and 0th-order efficiency (%) of each Example.

TABLE 3 Example 1 A B C D E F G FOV X direction (°) 34.9 47.2 60 66.773.7 81.1 88.9 Y direction (°) 34.9 47.2 60 66.7 73.7 81.1 88.9 Diagonal(°) 50.2 68.9 90 102.1 116.1 133.6 183.7 NA x 0.30 0.40 0.50 0.55 0.600.65 0.70 NA y 0.30 0.40 0.50 0.55 0.60 0.65 0.70 NA 0.42 0.57 0.71 0.780.85 0.92 0.99 Pitch x (μm) 28.33 21.25 17 15.45 14.17 13.08 12.14 Pitchy (μm) 28.33 21.25 17 15.45 14.17 13.08 12.14 Grating depth (nm) 494 500500 500 507 507 507 Effective refractive index of 1.976 1.979 1.9791.979 1.982 1.982 1.982 protrusions Total efficiency (%) 68.5 67 66.466.5 66.4 67 69 0th-order efficiency (%) 0.03 0.01 0.1 0.2 0.34 0.550.79

Here, the total efficiency (%) is defined as the sum of diffractionefficiency of diffraction light beams of a design order. For example,the case where diffraction light beams shown in FIG. 13 exit is assumed.In the figure, black circles indicate diffraction light beams of adesign order and white circles and a hatched circle indicate diffractionlight beams of orders (non-design orders) which are not designed. Thehatched circle indicates 0th-order light among the diffraction lightbeams of the non-design orders. In this case, the sum of diffractionefficiency of diffraction light beams indicated by the black circles inan FOV is employed as total efficiency without adding diffractionefficiency of the diffraction light beams indicated by the white circlesalthough they are within the FOV. On the other hand, the 0th-orderefficiency (0th-order light transmittance) means a ratio of a lightquantity of transmission 0th-order light that is a straight transmissioncomponent of the incident light to a light quantity of incident light.The total efficiency and the 0th-order efficiency shown in Table 3 arevalues calculated by RCWA on the basis of the configurations shown inTable 2.

As shown in Table 3, total efficiency that is 65% or more (morespecifically, 66% or more) and 0th-order efficiency that is lower than1% (more specifically, lower than 0.40%) are realized.

Example 2

This Example is a diffractive optical element 10 having a protrusion andrecess portion 12 having a multilayer structure that constitutes atwo-step protrusion and recess pattern and does not include a baseportion 123 like the example diffractive optical element 10 shown inFIG. 2A. However, also in this Example, an antireflection layer 14 isfurther provided on the surface of a substrate 11 opposite to itssurface on which the protrusion and recess portion 12 is formed (seeFIG. 8 ). More specifically, as shown in FIG. 2B and FIG. 2C, in thisExample, portions of an internal antireflection layer 13 constitute abottommost layer of the protrusions 121. However, these portionsconstituting parts of the protrusions 121 are 10 nm or less in thicknessand hence are not regarded as parts of the protrusions 121 but as partsof the internal antireflection layer 13. The design wavelength is 850 nmand the recesses 122 are air (n=1).

Also in this Example, protrusion and recess patterns were designed sothat the exit angle range θ_(out) (more specifically, diagonal viewingangle θ_(d)) of a diffraction light group that exits from the protrusionand recess portion 12 became equal to 50°, 68°, 90°, 102°, 116°, 134°,and 164°, respectively. The Examples whose θ_(d) is 50°, 68°, 90°, 102°,116°, 134°, and 164° are Examples 2A, 2B, 2C, 2D, 2E, 2F, and 2G,respectively. Example 2G is a Referential Example.

In this Example, the material of the protrusion and recess portion 12was a four-layer multilayer film made of Ta₂O₅ having a refractive indexof 2.192 and SiO₂ having a refractive index of 1.463. The material ofthe internal antireflection layer 13 was a single-layer dielectric filmmade of similar SiO₂. This Example is the same as Example 1 in the otherrespects. Table 4 shows specific configurations of Examples 2A to 2G ofthe diffractive optical element 10 of this Example. As shown in Table 4,in this Example, Examples 2A to 2G are the same in configuration exceptthe structure of the protrusions 121.

TABLE 4 Thickness (nm) Refractive Example 2 Configuration Material(s)index A B C D E F G Antireflection SiO₂ 1.463 172 layer Ta₂O₅ 2.192 67SiO₂ 1.463 42 Ta₂O₅ 2.192 18 SiO₂ 1.463 35 Ta₂O₅ 2.192 18 SubstrateBorosilicate 1.514 — glass Internal SiO₂ 1.463 145 antireflection layerProtrusion Protrusions Ta₂O₅ 2.192 35 35 35 35 35 35 35 and recess SiO₂1.463 49 49 49 49 49 49 49 portion Ta₂O₅ 2.192 295 295 295 295 301 301301 SiO₂ 1.463 146 146 146 146 146 146 146

A manufacturing method of this Example is as follows. First, anantireflection layer 14 that is the same as in Example 1 is formed on aglass substrate. The material and thickness of each layer are as shownin Table 4.

Then an SiO₂ film to function as an internal antireflection layer 13 isformed at a thickness 145 nm on the surface of the glass substrateopposite to its surface on which the antireflection layer 14 has beenformed. Then a four-layer dielectric multilayer film is formed at apredetermined film thickness using Ta₂O₅ and SiO₂ as materials of aprotrusion and recess portion 12. The structure and the film thicknessof each layer of the protrusion and recess portion 12 of each Exampleare as shown in Table 4.

Subsequently, the thus-formed four-layer multilayer film made of SiO₂and Ta₂O₅ are processed into a two-step protrusion and recess structureby photolithography and etching. The heights (grating depths) of theprotrusions 121 of the respective Examples are 525 nm to 531 nm (thesums of the thicknesses of the protrusion materials shown in Table 4). Aheight d (film thickness) of the protrusions 121 can be measured byobservation of a cross section using a step gauge or an SEM. In thismanner, diffractive optical elements 10 of Examples 2A-2G are obtained.

Table 5 shows detailed data of optical characteristics of Examples2A-2G. Table 5 shows FOVs (°) corresponding to exit angle ranges in theX direction, Y direction, and diagonal direction of exiting light, NAs,a grating depth (nm) of the protrusions 121, an effective refractiveindex of the materials of the protrusions 121, total efficiency (%), and0th-order efficiency (%) of each Example. The total efficiency and the0th-order efficiency shown in Table 5 are values calculated by RCWA onthe basis of the configurations shown in Table 4.

TABLE 5 Example 2 A B C D E F G FOV X direction (°) 34.9 47.2 60 66.773.7 81.1 88.9 Y direction (°) 34.9 47.2 60 66.7 73.7 81.1 88.9 Diagonal(°) 50.2 68.9 90 102.1 116.1 133.6 183.7 NA x 0.30 0.40 0.50 0.55 0.600.65 0.70 NA y 0.30 0.40 0.50 0.55 0.60 0.65 0.70 NA 0.42 0.57 0.71 0.780.85 0.92 0.99 Pitch x (μm) 28.33 21.25 17 15.45 14.17 13.08 12.14 Pitchy (μm) 28.33 21.25 17 15.45 14.17 13.08 12.14 Grating depth (nm) 525 525525 525 531 531 531 Effective refractive index of 1.921 1.921 1.9211.921 1.924 1.924 1.924 protrusions Total efficiency (%) 72.2 71.2 70.270.1 70 71.1 72.8 0th-order efficiency (%) 0.13 0.02 0.02 0.09 0.19 0.370.57

As shown in Table 5, total efficiency that is 70% or more and 0th-orderefficiency that is lower than 1% (more specifically, lower than 0.40%)are realized.

Comparative Example 1

This Example is Comparative Examples for Example 1. These ComparativeExamples are example diffractive optical elements that were designedusing the same kinds of members (substrate 11, antireflection layer 14,and internal antireflection layer 13) as the respective example ofdiffractive optical elements 10 of Example 1 so as to have the same exitangle ranges as the respective example of diffractive optical elements10 of Example 1 have. However, this Example is different from Example 1in that the protrusions 121 is configured to be a single layer (morespecifically, a single layer made of only Ta₂O₅ having a refractiveindex 2.192). That is, these Comparative Examples are different fromExample 1 in that the low-refractive index material (SiO₂) that isemployed in the protrusions 121 of Example 1 is not employed toconstitute a topmost layer of the protrusions 121. Also in this Example,the design wavelength is 850 nm and the recesses 122 are air (n=1). ThisExample is the same as Example 1 in the other respects. Table 6 showsspecific configurations of Comparative Examples 1A to 1G of thediffractive optical element of this Comparative Example. As shown inTable 6, in this Example, Comparative Examples 1A to 1G are the same inconfiguration except the structure of the protrusions 121.

TABLE 6 Thickness (nm) Refractive Comparative Example 1 ConfigurationMaterial(s) index A B C D E F G Antireflection SiO₂ 1.463 172 layerTa₂O₅ 2.192 67 SiO₂ 1.463 42 Ta₂O₅ 2.192 18 SiO₂ 1.463 35 Ta₂O₅ 2.192 18Substrate Borosilicate 1.514 — glass Internal Ta₂O₅ 2.192 19antireflection SiO₂ 1.463 34 layer Ta₂O₅ 2.192 25 SiO₂ 1.463 26Protrusion Base portion Ta₂O₅ 2.192 200 and recess Protrusions 406 406414 414 414 414 414 portion

Table 7 shows detailed data of optical characteristics of ComparativeExamples 1A-1G. Table 7 shows FOVs (°) corresponding to exit angleranges in the X direction, Y direction, and diagonal direction ofexiting light, NAs, a grating depth (nm) of the protrusions 121, aneffective refractive index of the material of the protrusions 121, totalefficiency (%), and 0th-order efficiency (%) of each Example. The totalefficiency and the 0th-order efficiency shown in Table 7 are valuescalculated by RCWA on the basis of the configurations shown in Table 6.

TABLE 7 Comparative Example 1 A B C D E F G FOV X direction (°) 34.947.2 60 66.7 73.7 81.1 88.9 Y direction (°) 34.9 47.2 60 66.7 73.7 81.188.9 Diagonal (°) 50.2 68.9 90 102.1 116.1 133.6 183.7 NA x 0.30 0.400.50 0.55 0.60 0.65 0.70 NA y 0.30 0.40 0.50 0.55 0.60 0.65 0.70 NA 0.420.57 0.71 0.78 0.85 0.92 0.99 Pitch x (μm) 28.33 21.25 17 15.45 14.1713.08 12.14 Pitch y (μm) 28.33 21.25 17 15.45 14.17 13.08 12.14 Gratingdepth (nm) 406 406 414 414 414 414 414 Effective refractive index of2.192 2.192 2.192 2.192 2.192 2.192 2.192 protrusions Total efficiency(%) 63.9 63.1 61.6 61.2 61.1 61.6 62.6 0th-order efficiency (%) 0.190.09 0.01 0.01 0.03 0.12 0.25

As shown in Table 7, in each Example the total efficiency is lower than65% (more specifically, lower than 64%) although the 0th-orderefficiency is as low as 1% or less (more specifically, 0.3% or less). Itis understood that the diffraction efficiency is inferior to that inExample 1.

The above-described 0th-order efficiency and total efficiency of therespective Examples are shown together in graphs of FIG. 14 and FIG. 15, respectively. FIG. 14 is a graph showing relationships between the NAand the 0th-order efficiency of each of Example 1, Example 2, andComparative Example 1. FIG. 15 is a graph showing relationships betweenthe NA and the total efficiency of each of Example 1, Example 2, andComparative Example 1.

As shown in FIG. 14 and FIG. 15 , the diffractive optical elements ofExamples in which the exit angle range θ_(out) is 50° or more (NA is 0.3or more) can realize 0th-order efficiency at the design wavelength thatis lower than 1.0% and total efficiency at the design wavelength that is65% or more. Furthermore, the diffractive optical elements of Examplesin which the exit angle range θ_(out) is 50° or more and 130° or less(more specifically, NA is 0.3 to 0.65) can realize 0th-order efficiencyat the design wavelength that is lower than 0.5% (more specifically,lower than 0.4%) and total efficiency at the design wavelength that is65% or more.

The diffractive optical elements of Example 2 in which the protrusions121 have a multilayer structure of four or more layers and the exitangle range θ_(out) is 50° or more and 140° or less (more specifically,NA is 0.3 to 0.65) can realize 0th-order efficiency at the designwavelength that is lower than 0.5% (more specifically, lower than 0.4%)and total efficiency at the design wavelength that is 70% or more.Furthermore, the diffractive optical elements of Example 2 in which theexit angle range θ_(out) is 50° or more and 130° or less (morespecifically, NA is 0.3 to 0.60) can realize 0th-order efficiency at thedesign wavelength lower than 0.2% and total efficiency at the designwavelength that is 70% or more.

The above effects can be realized while the height of the protrusions121 is prevented from becoming large as exemplified by the grating depthat the design wavelength of 850 nm being 600 nm or less (morespecifically, 550 nm or less). Therefore, the invention can alsocontribute to thinning of optical elements.

INDUSTRIAL APPLICABILITY

The invention can be applied suitably to uses for widening theillumination range of a predetermined light pattern that is formed by adiffraction grating while reducing 0th-order light.

Although the invention has been described in detail with reference tothe particular embodiments, it is apparent to those skilled in the artthat various changes and modifications can be made without departingfrom the spirit and scope of the invention.

The present application is based on Japanese Patent Application No.2018-110909 filed on Jun. 11, 2018, the disclosure of which isincorporated herein by reference.

REFERENCE SIGNS LIST

-   10: Diffractive optical element-   11: Substrate-   12: Protrusion and recess portion-   121: Protrusions-   122: Recesses-   123: Base portion-   13: Internal antireflection layer-   14: Antireflection layer-   21: Light beam-   22: Diffraction light beam group-   23: Light spot

The invention claimed is:
 1. A diffractive optical element comprising: asubstrate; a protrusion and recess portion that is formed on one surfaceof the substrate and imposes predetermined diffraction on incidentlight; and an antireflection layer provided between the substrate andthe protrusion and recess portion, wherein: an effective refractiveindex difference Δn in a wavelength range of the incident light betweena first medium constituting a protrusion of the protrusion and recessportion and a second medium constituting a recess of the protrusion andrecess portion is 0.70 or more; an exit angle range θ_(out) ofdiffraction light exiting from the protrusion and recess portion whenthe incident light enters the substrate from a normal direction of thesubstrate is 60° or more; and total efficiency of diffraction lightexiting from the protrusion and recess portion in the exit angle rangewith respect to a quantity of entire light entering the protrusion andrecess portion in the wavelength range of the incident light is 65% ormore.
 2. The diffractive optical element according to claim 1, wherein:the second medium is air; and an effective refractive index of the firstmedium in the wavelength range of the incident light is 1.70 or more. 3.The diffractive optical element according to claim 1, wherein: the firstmedium is a multilayer film comprising two or more layers made of two ormore materials having different refractive indexes; and a topmost layerof the protrusion is made of a low-refractive index material among thematerials constituting the multilayer film.
 4. The diffractive opticalelement according to claim 1, wherein the Δn and the θ_(out) satisfy arelationship of Δn/sin(θ_(out)/2)≥1.0.
 5. The diffractive opticalelement according to claim 1, wherein 0th-order efficiency of theprotrusion and recess portion in the wavelength range of the incidentlight is lower than 3.0%.
 6. The diffractive optical element accordingto claim 5, wherein a ratio of a light quantity of 0th-order light to aquantity of entire light exiting from the protrusion and recess portionin the wavelength range of the incident light is lower than 1.0%.
 7. Thediffractive optical element according to claim 1, wherein: the exitangle range is smaller than 140°; 0th-order efficiency of the protrusionand recess portion in the wavelength range of the incident light is 0.5%or lower; and the total efficiency of the diffraction light exiting fromthe protrusion and recess portion in the exit angle range with respectto the quantity of the entire light entering the protrusion and recessportion in the wavelength range of the incident light is 70% or more. 8.The diffractive optical element according to claim 1, wherein the firstmedium is entirely made of an inorganic material.
 9. The diffractiveoptical element according to claim 1, further comprising, at leastbetween the recess and the antireflection layer, a base portion made ofsame material as a bottommost layer of the protrusion.
 10. Thediffractive optical element according to claim 1, wherein: theantireflection layer is a dielectric multilayer film; and reflectance ofthe antireflection layer for at least particular polarized light in thewavelength range of the incident light, exiting from the element at anangle being ¼ of the exit angle range with respect to a normal directionof the substrate, is 0.5% or less.
 11. The diffractive optical elementaccording to claim 1, wherein reflectance of the antireflection layerfor at least particular polarized light in the wavelength range of theincident light, incident on the antireflection layer at 40° or less withrespect to a normal direction of the substrate, is 0.5% or less.
 12. Thediffractive optical element according to claim 1, wherein: the incidentlight is light in at least a part of a wavelength range of 700 nm to1,200 nm; and reflectance of the antireflection layer for at leastparticular polarized light in a wavelength range of 360 nm to 370 nm,incident on the antireflection layer at 20° or less with respect to anormal direction of the substrate, is 1.0% or less.
 13. The diffractiveoptical element according to claim 1, further comprising a secondantireflection layer on a surface of the substrate opposite to thesurface on which the protrusion and recess portion is formed.
 14. Thediffractive optical element according to claim 13, wherein reflectanceof the second antireflection layer for at least particular polarizedlight in the wavelength range of the incident light, exiting from theelement at an angle being ¼ of the exit angle range with respect to anormal direction of the substrate, is 0.5% or less.
 15. A projectiondevice comprising: a light source; and the diffractive optical elementaccording to claim 1, wherein a ratio of a light quantity of lightirradiating a predetermined projection surface to a light quantity oflight emitted from the light source is 50% or more.
 16. A measurementdevice comprising: a projection unit configured to emit inspectionlight; and a detection unit configured to detect scattering lightgenerated as a result of irradiation of the inspection light emittedfrom the projection unit to a measurement target object, wherein theprojection device according to claim 15 is provided as the projectionunit.